Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading Introduction Prof. ing

Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading

IntroductionProf. ing. Claudio di Prisco

2

Prof. ing. Claudio di Prisco

Indice

Outlook of the presentationOutlook of the presentation

a) Introduction

b) Failure mechanisms and punching

c) The macro-element concept

d) Cyclic soil-structure interaction: constitutive modeling observations

e) A simplified approach

3


Definitions: shallow foundations

GEOMETRIESGEOMETRIES

• Shallow (B/H>4) and deep foundations (B/H<4)

• Strip footings

• Mat foundations

• Grid foundations

Lancellotta e Calavera, 1999

4


The soil-structure interaction

Statically determinate interaction

Redundantly constrained interaction

5


What are the consequences? Irreversible differential settlements, damage to the structureenergy dissipation

The soil structure interaction

site amplification

Depending on topography and stratigraphy

Soil- foundation interaction

Dynamic structural response

3

1

2

4

6


1. The pseudo-static approach: the rigid-plastic approach

Static equivalent horizontal load: step 2 is disregarded whereas step 4 is abruptly simplified.

A design pseudo-static distribution of forces is applied to the structure, additional loads H and M are applied on the foundation and new limit conditions have to be accounted for

In this perspective the design of the shallow foundation under inclined and eccentric loads become essential

7


Failure mechanisms: the interaction domain in quasi static conditions

Failure mechanisms: Failure mechanisms: small scale 2D experimental test results (drained and small scale 2D experimental test results (drained and undrained conditions, cohesive and granular soils)undrained conditions, cohesive and granular soils)

Nova e Montrasio, 1988

8


Punching mechanisms

Punching mechanisms and 2nd order effectsPunching mechanisms and 2nd order effects

Lancellotta e Calavera, 1999

Lancellotta, 1993

9


The limit analysis

The limit analysis and the Prandtl mechanismThe limit analysis and the Prandtl mechanism

• Rigid-plastic mechanical behavior of the material• Associated flow-rule• Mohr-Coulomb failure criterion

The kinematic limit analysis approachThe kinematic limit analysis approach

Lancellotta, 1993

Nova, 2008

10


The Terzaghi Theory

The Terzaghi bearing capacity equation for vertical and centered The Terzaghi bearing capacity equation for vertical and centered loadsloads

Lancellotta, 1993

1

2LIM c qq B N cN qN

( ')

( ')

( ')c c

q q

N N

N N

N N

11


Inclined and eccentric loads: Brinch-Hansen coefficientsInclined and eccentric loads: Brinch-Hansen coefficients

Lancellotta, 1993

H/M

V

12


The interaction domain for rigid shallow footings

m = M/ψBVMAX,

h = H/μVMAX

ξ = V/VMAX

1. To each point belonging to the failure locus a distinct failure mechanism corresponds

2. Difficulty in defining the failure locus when loose sand strata are concerned

3. Extension to rectangular footings

4. Extension for D/B>0

5.

MONOTONOUSLY INCREASING LOADING

22 2

2 1 0c

M H Vf V

B V

13


Centered vertical load Centered inclined load

Elasto-plastic finite element numerical analyses

Tochnog perfect elasto-plastic numerical analyses

14


The uplift

Shirato et al. 2007

15


The uplift of rigid shallow foundations

Confronto tra il Dominio di Interazione fornito dal modello Nova- Montrasio e i valori puntuali valutati con il modello numerico

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700 800 900 1000

V[kN/m]

M [

kN

m/m

]

Modello Elasto-Plastico

Modello Nova-Montrasio

Poli. (Modello Nova-Montrasio)

16


M

HV

Q

qv

u

Inclined LOADS

Rigid strip footing

0

0

1

2

3

4

H

V

Dense sand

B

0.5B

0.5B

0.5B

INTERACTION DIAGRAMS

GENERALISED STRESS PATHS

LOAD CONTROLLED TESTS

THE EXPERIMENTAL TEST SERIES

17


Failure mechanism

in unreinforced dense sand layer

Failure mechanism

in unfastened reinforced dense sand layer

DENSE SAND, vertical loading

18


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45 50 55 60 65

v [mm]

V [ kPa]

Unreinforced

Unfastened reinforced

fastened reinforced

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45

u [mm]

H [ kPa]

H/V = 0.1

Sabbia sciolta non rinforzata

0

2

4

6

0 10 20 30 40 50V [kPa]

H [

kP

a]

Sabbia sciolta rinforzata con geosintetici non allacciati

0

2

4

6

8

10

0 20 40 60 80 100 120 140

V [kPa]

H [

kP

a]

Sabbia sciolta rinforzata con geosintetici allacciati

0

5

10

15

20

25

-20 0 20 40 60 80 100 120 140 160 180 200

V [kPa]

H [

kP

a]

EXPERIMETNAL DATA and NUMERICAL INTERPOLATION

INTERACTION DIAGRAMS

Unreinforced loose sand Unfastened reinforced loose sand

Fastened reinforced loose sand

20


Numerical simulations Tochnnog finite element codeelasto-perfectly plastic constitutive model

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

0 0,05 0,1 0,15 0,2 0,25 0,3

v / B

V /

VM

AX

Legge associata

Legge non associata

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,2 0,4 0,6 0,8 1 1,2 1,4

u [m]

v [

m]

mohr-coulomb associata

mohr-coulomb non associata

Non associated flow rule ( = 0)

Truss elements

21


1

2

4

K =k() ?

= () ?

The visco-elastic approach

22


M - curves

-0.08 -0.04 0 0.04 0.08-0 .1 -0 .06 -0 .02 0.02 0.06 0.1

(rad)

- 2

- 1

0

1

2

-1 .5

-0 .5

0.5

1.5

M (

kN.m

)

-0.08 -0.04 0 0.04 0.08-0 .1 -0 .06 -0 .02 0.02 0.06 0.1

(rad)

- 2

- 1

0

1

2

-1 .5

-0 .5

0.5

1.5

M (

kN.m

)

PWRI experimental test results,2005

Dense sand stratum Loose sand stratum

FOOTING UPLIFT

23


24


Cross section

Plan view

Ispra Laboratory Elsa (Pedretti, 1998)

Ispra Laboratory Elsa di Elsa di (Pedretti, 1998)

25


26


27


28


29


A simplified approach

A sA symmetricymmetric generalised stress-paths generalised stress-paths

1E-005 0.0001 0.001 0.01 0.1

(rad)

0

0.2

0.4

0.6

0.8

1

0.1

0.3

0.5

0.7

0.9

Kf

/ Kf,

0 (-

)

1E-005 0.0001 0.001 0.01 0.1 1

(rad)

0

0.1

0.2

0.3

0.4

0.5

0.05

0.15

0.25

0.35

0.45

f (

-)

Medium Relative DensityDR = 50-60%

ISPR A phase 1

ISPR A phase 2

ISPR A phase 3

N um erica l phase 1

N um erica l phase 2

PW R I test n .10

PW R I test n .11

c) Rotational SecantStiffness

d) Damping Factor

30


1E-005 0.0001 0.001 0.01 0.1rocking angle (rad)

0

0.2

0.4

0.6

0.8

1

K/K0(-)

1E-005 0.0001 0.001 0.01displacement (m)

0

0.2

0.4

0.6

0.8

1

K/K0(-)

0.0001 0.001 0.01 0.1rocking angle (rad)

0

0.1

0.2

0.3

0.4

0.5

(-)

High relative densityDR = 90%

ISPRA phase 1ISPRA phase 2ISPRA phase 3

numerical phase 1numerical phase 2PWRI test n. 5PWRI test n. 8

Rotational SecantStiffness

Translational SecantStiffness

Damping Factor

Documents

Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic and cyclic loading Introduction Prof. ing